Fourier Series of simple function.

Tschew
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f(x) = cos(x) x from [-PI, 0]
f(x) = -cos(x) x from ] 0, PI]

I'm not sure how to deal with getting a Fourier series for this function. (don't bother explaining theory, I know that, just can't apply it in this case) Could anyone help me out?
 
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okay, I think I got it!

Ah well, what a stupid question that was. I figured it out.. now I just need to see what happens for even and odd harmonics and that'll be that. Thanks.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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